1. Field of the Invention
The present invention relates to a method to determine the usefulness of alignment marks to correct overlay, and to a combination of a lithographic apparatus and an overlay measurement system capable of carrying out said method.
2. Description of the Related Art
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
When multiple patterns are transferred subsequently to a substrate, it may be desired to align subsequent patterns relative to each other. To align a subsequent pattern to a previously transferred pattern it is important to know the location of the previously transferred pattern. In order to determine the location of a pattern on a wafer, alignment marks are transferred to predefined positions on the substrate as part of said pattern. By measuring the position of the alignment marks, information can be obtained which can be used to transfer a subsequent pattern relative to the previously transferred pattern to the substrate.
The position information of a previously transferred pattern required for accurately transferring a subsequent pattern relative to the previously transferred pattern usually does not correspond one to one to the position information obtained from measuring the position of the alignment marks, as not all areas of a pattern can be used to place alignment marks. As a consequence, alignment marks are usually placed at edges of a pattern or in so-called scribe-lanes, while it is important that the center regions of the pattern used to manufacture devices are aligned with respect to each other.
To solve this, a model can be fitted to the measured positions of the alignment marks. This model can then be used to estimate the position information of a previously transferred pattern that can be used to accurately transfer a subsequent pattern relative to the previously transferred pattern.
For instance, an alignment mark may be positioned at a nominal position (xc, yc). Measuring the position of the alignment mark and comparing the measured position with the nominal position may result in a displacement of the alignment mark by (dx, dy) from the nominal position. This displacement may be used to predict the displacement in every point on the substrate by using a linear 6 parameter model in which the displacement is described in terms of translation, magnification and rotation. For each measurement of one alignment mark, the following equations can be formed:Mx·xc−Ry·yc+Cx=dx Rx·xc−My·yc+Cy=dy where xc en yc are the coordinates of the nominal position where the measurement is done, Cx is a translation in x-direction, Cy is a translation in y-direction, Mx is a magnification in x-direction, My is a magnification in y-direction, Rx is a rotation of the x-axis about the z-axis, Ry is a rotation of the y-axis about the z-axis, and dx, dy are the displacement of the alignment mark from the nominal position in respectively the x- and y-direction.
Writing these equations for every mark on the substrate leads to the following system:
            [                                                  dx              i                                                                          dy              i                                          ]        =                                        [                                                            1                                                                      xc                    i                                                                                        -                                          yc                      i                                                                                        0                                                  0                                                  0                                                                              0                                                  0                                                  0                                                  1                                                                      yc                    i                                                                                        xc                    i                                                                        ]                    ⁡                      [                                                            Cx                                                                              Mx                                                                              Rx                                                                              Cy                                                                              My                                                                              Ry                                                      ]                          ⁢                                  ⁢        i            =      1        ,  …  ⁢          ,  NIn matrix vector notations it looks like b=A·x and matrix A has size 2N×6, where N is the number of alignment marks used.
To be able to find the model parameters to fit (Cx, Cy, Mx, My, Rx and Ry) at least 6 of these equations (i.e. 3 measurements) are needed. Normally, more measurements than parameters are available. This leads to solving an over-determined system of equations, wherein the matrix has more rows than columns. A solution of these equations can be found using the well-known Least Square Method. This can be written as x=(ATA)−ATb).
In order to determine how successful the alignment between two subsequently transferred patterns was, i.e. in order to determine the overlay between two subsequently transferred patterns, both patterns are provided with corresponding overlay marks, so that the position of an overlay mark in one pattern can be measured relative to a corresponding overlay mark of the other pattern.
Overlay is expressed in terms of overlay error, which expresses the deviation of a point in one of the patterns from a perfect alignment with a corresponding point in another layer.
Consequently, perfect overlay results in a zero overlay error, and non-zero overlay errors indicate that the overlay is not perfect. A non-zero overlay error may result from the following error sources.                measurement error in the measuring of the position of an alignment mark, e.g. process induced errors, such as asymmetry, etc.;        placement error in placing the alignment mark at the nominal position, e.g. due to random variations in temperature, pressure, etc.;        measurement error in measuring the overlay error, which can be split into placement error in placing the overlay marks and measurement error in measuring the position of an overlay mark in one pattern relative to a corresponding overlay mark in the other pattern; and        model error in fitting the model to the measured displacements of the alignment marks.        
Using more measurement data for the earlier described linear model in order to deal with the abovementioned error sources will not improve the accuracy of the model and may lead to productivity loss. Using more measurement data has the advantage that random or semi-random errors in the data are averaged out, so that these errors do not have a large contribution to the overlay.
The model errors, which may have the largest contribution compared to the other error sources, can be dealt with by improving the model, e.g. by using a more advanced alignment model. Different models have been proposed to use instead of the linear model, examples of which are higher order polynomial models, radial basis functions, and extended zone alignment.
However, when such more advanced alignment models are used the contribution of the other error sources to the overlay error becomes more significant, because there is less averaging out. In other words, the performance of every alignment mark has a direct impact on overlay around the location of this alignment mark. As a result thereof, switching to a more advanced model may not result in an improved overlay.
Hence, it becomes more critical to optimally choose alignment mark location and to only use properly functioning alignment marks, which means that in practice, it may be desirable that only the alignment marks are used of which the measured displacement is a good representation of the actual displacement of the alignment mark.